Finite Group Databasebeta

← D3×#65834 #14481758

Subgroups — D3×#65834 #14481758

Order 1920.

2160 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756259C211yesmaximal, characteristic, complemented
2C2×C5×D3×C4⋊C4C211yesmaximal, characteristic
3C3×#65834C211yesmaximal, characteristic, complemented
4#11754619C212yesmaximal, complemented
5D3×#4072C212yesmaximal
6D3×#4070C214yesmaximal
7#11754182C214yesmaximal, complemented
8D3×#4036C214yesmaximal, complemented
9D3×#4034C214yesmaximal, complemented
10#11753370C214yesmaximal, complemented
11#11753331C214yesmaximal, complemented
12C2×#65834—31nomaximal, Hall
13C22×C4×C5×D3C2212yes—
14C22×C4×C5×D3C2211yescharacteristic
15C2×D3×Dic10C2214yes—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17#91815C2212yes—
18#91813C2214yes—
19#91779C2214yescomplemented
20#91777C2214yescomplemented
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C5×Dic3⋊C4C2212yes—
23C5×D3×C4⋊C4C2214yes—
24C5×D3×C4⋊C4C2214yes—
25C3×#4072C2212yes—
26C3×#4070C2214yes—
27C3×#4036C2214yescomplemented
28C3×#4034C2214yescomplemented
29#91575C2218yes—
30D3×C22⋊Dic5C2214yes—
31#91529C2214yes—
32#91470C2214yescomplemented
33#91468C2214yescomplemented
34D3×C4⋊Dic5C2214yes—
35D3×C4⋊Dic5C2212yes—
36D3×C4⋊Dic5C2212yes—
37D3×#683C2218yes—
38C4×D3×Dic5C2214yes—
39#91388C2214yescomplemented
40#91384C2214yescomplemented
41#91371C2214yes—
42#91369C2214yes—
43#91365C2214yes—
44#91352C2218yes—
45#91346C2218yescomplemented
46#91343C2218yescomplemented
47#91338C2212yes—
48#91338C2212yes—
49#91328C2218yescomplemented
50#91327C2218yescomplemented
51D3×#544—51nomaximal, Hall
52C22×C5×C4⋊C4—31no—
53C2×#4072—32no—
54C2×#4070—34no—
55#65834—32no—
56#65834—34no—
57#65834—34no—
58#65834—34no—
59#65834—31no—
60#65834D311yescharacteristic, direct product factor
61C2×#4036—34no—
62C2×#4034—34no—
63C23×C5×D3C2311yescharacteristic
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C2×Dic30C2314yes—
67C22×C5×Dic3C2312yes—
68C22×C5×Dic3C2311yescharacteristic
69C2×C4×C5×D3—44no—
70C2×C4×C5×D3Q818yescomplemented
71C2×C4×C5×D3C2314yes—
72C2×C4×C5×D3C2314yes—
73C2×C4×C5×D3C2312yes—
74C2×C4×C5×D3C2312yes—
75C2×C3×Dic10C2314yes—
76C2×#1204C2318yes—
77C2×D3×Dic5C2314yes—
78C2×D3×Dic5C2314yes—
79D3×Dic10—48no—
80C3×C5×C4⋊C4C2314yes—
81#6719C2314yes—
82C4⋊Dic15C2312yes—
83C4⋊Dic15C2314yes—
84C4⋊Dic15C2312yes—
85#6712C2318yes—
86C4×Dic15C2314yes—
87C5×C4⋊Dic3C2314yes—
88C5×Dic3⋊C4C2318yes—
89C3×C22⋊Dic5C2314yes—
90C3×C4⋊Dic5C2312yes—
91C3×C4⋊Dic5C2312yes—
92C3×C4⋊Dic5C2314yes—
93C3×#683C2318yes—
94C3×C4×Dic5C2314yes—
95Dic3⋊Dic5C2314yes—
96Dic3⋊Dic5C2314yes—
97Dic3⋊Dic5C2318yes—
98#6669C2318yes—
99#6668C2318yes—
100(C2×D3)⋊Dic5C2314yes—
101(C2×D3)⋊Dic5C2314yes—
102Dic3×Dic5C2314yes—
103Dic3×Dic5C2314yes—
104C3×#544—51no—
105#5729—54no—
106D3×C4⋊Q8—54no—
107#5689—54no—
108D3×#125—54no—
109D3×C22⋊Q8—54no—
110#5623—54no—
111D3×#117—52no—
112#5519—52no—
113C2×D3×C4⋊C4D511yescharacteristic
114#5500—51no—
115C23×C4×C5—31no—
116C23×C4×C5—32no—
117C22×Dic10—34no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—31no—
120C2×C5×C4⋊C4—34no—
121C2×C5×C4⋊C4—34no—
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C22⋊Dic5—34no—
124#4072—32no—
125#4072—34no—
126#4072—32no—
127#4072—32no—
128#4072—34no—
129#4072C2×D312yes—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5—34no—
132C2×C4⋊Dic5—32no—
133#4070—34no—
134#4070—34no—
135#4070—38no—
136#4070—34no—
137#4070—38no—
138#4070C2×D314yes—
139C2×#683—38no—
140C2×C4×Dic5—34no—
141#4036—34no—
142#4036—38no—
143#4036—34no—
144#4036—38no—
145#4036—34no—
146#4036C2×D314yescomplemented
147#4034—38no—
148#4034—34no—
149#4034—34no—
150#4034—38no—
151#4034—34no—
152#4034C2×D314yescomplemented
153C2×#544—151noSylow
154C23×C3×C5C2411yescharacteristic
155C22×C5×D3—22no—
156C22×C5×D3—22no—
157C22×C5×D3C2×Q814yes—
158C22×C5×D3C2411yescharacteristic
159C22×C5×D3C2411yescharacteristic
160C2×C3×C4×C5—42no—
161C2×C3×C4×C5C2×Q814yescomplemented
162C2×C3×C4×C5C2414yes—
163C2×C3×C4×C5C2412yes—
164C2×Dic15C2414yes—
165C2×Dic15C2414yes—
166Dic30—44no—
167C2×C5×Dic3—42no—
168C2×C5×Dic3C2×Q814yescomplemented
169C2×C5×Dic3C2414yes—
170C2×C5×Dic3C2412yes—
171C4×C5×D3—28no—
172C4×C5×D3—44no—
173C4×C5×D3C2×Q818yes—
174C4×C5×D3C2×Q818yescomplemented
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2414yes—
177C3×Dic10—44no—
178#1204—48no—
179D3×Dic5—28no—
180D3×Dic5—28no—
181C2×D3×Q8—54no—
182C22×C4×D3C2×D512yes—
183C22×C4×D3C2×D511yescharacteristic
184C3×C4⋊Q8—54no—
185C3×#125—54no—
186C3×C22⋊Q8—54no—
187C3×#117—52no—
188C2×C3×C4⋊C4C2×D511yescharacteristic
189#946—54no—
190#944—58no—
191#926—52no—
192C2×C4⋊Dic3C2×D511yescharacteristic
193#924—54no—
194C2×Dic3⋊C4C2×D512yes—
195#897—54no—
196#896—58no—
197#892—52no—
198#892—52no—
199D3×C4⋊C4—58no—
200D3×C4⋊C4—52no—
201D3×C4⋊C4—54no—
202D3×C4⋊C4—52no—
203D3×C4⋊C4C2×D514yes—
204D3×C4⋊C4C2×D514yes—
205#890—54no—
206#890—54no—
207#889—58no—
208#889—58no—
209#888—54no—
210#888—54no—
211#888—58no—
212D3×C22⋊C4—54no—
213#878—58no—
214#877—54no—
215#872—54no—
216C42×D3—54no—
217#870—54no—
218#869—54no—
219C24×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—38no—
222C22×C4×C5—32no—
223C22×C4×C5—32no—
224C22×C4×C5—32no—
225C22×C4×C5—34no—
226C22×C4×C5—34no—
227C22×C4×C5—124no—
228C22×C4×C5C22×D312yes—
229C22×C4×C5C22×D311yescharacteristic
230C22×Dic5—34no—
231C22×Dic5—34no—
232C2×Dic10—34no—
233C2×Dic10—38no—
234C2×Dic10—128no—
235C2×Dic10C22×D314yes—
236C5×C4⋊C4—38no—
237C5×C4⋊C4—34no—
238C5×C4⋊C4C22×D314yes—
239C22⋊Dic5—34no—
240C22⋊Dic5—34no—
241C22⋊Dic5—34no—
242C22⋊Dic5C22×D314yes—
243C4⋊Dic5—32no—
244C4⋊Dic5—34no—
245C4⋊Dic5—32no—
246C4⋊Dic5—34no—
247C4⋊Dic5—38no—
248C4⋊Dic5—34no—
249C4⋊Dic5C22×D312yes—
250C4⋊Dic5C22×D314yes—
251C4⋊Dic5C22×D312yes—
252#683—38no—
253#683—38no—
254#683—38no—
255#683C22×D318yes—
256C4×Dic5—34no—
257C4×Dic5—34no—
258C4×Dic5—34no—
259C4×Dic5C22×D314yes—
260#544—51no—
261#544—152no—
262#544—154no—
263#544—154no—
264#544—154no—
265#544—151no—
266C2×C4⋊Q8—154no—
267C2×#125—154no—
268C2×C22⋊Q8—154no—
269C2×#117—152no—
270C22×C4⋊C4—31no—
271C22×C3×C5—21no—
272C22×C3×C5—21no—
273C22×C3×C5C22×Q812yes—
274C22×C3×C5C2511yescharacteristic
275C2×C5×D3—21no—
276C2×C5×D3—21no—
277C2×C5×D3—28no—
278C2×C5×D3C22×Q812yes—
279C2×C5×D3C22×Q812yes—
280C2×C5×D3H(5,𝔽2)12yes—
281C2×C5×D32−1+412yes—
282C3×C4×C5—24no—
283C3×C4×C5C22×Q814yes—
284Dic15—24no—
285Dic15—24no—
286C3×Dic5—24no—
287C3×Dic5—24no—
288C5×Dic3—24no—
289C5×Dic3C22×Q814yes—
290C23×D3C22×D511yescharacteristic
291C2×C3×Q8—54no—
292C22×C3×C4C22×D512yes—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3C22×D512yes—
295C22×Dic3C22×D511yescharacteristic
296D3×Q8—208no—
297C2×C4×D3—44no—
298C2×C4×D3—54no—
299C2×C4×D3—54no—
300C2×C4×D3Dic1018yescomplemented
301C2×C4×D3C22×D514yes—
302C2×C4×D3C22×D514yes—
303C2×C4×D3C22×D512yes—
304C2×C4×D3C22×D512yes—
305C2×Dic6—54no—
306C2×Dic6—58no—
307C3×C4⋊C4—58no—
308C3×C4⋊C4—52no—
309C3×C4⋊C4—54no—
310C3×C4⋊C4—52no—
311C3×C4⋊C4C22×D514yes—
312C3×C22⋊C4—54no—
313C3×C42—54no—
314#217—54no—
315(C2×D3)⋊C4—54no—
316(C2×D3)⋊C4—54no—
317C4⋊Dic3—52no—
318C4⋊Dic3—52no—
319C4⋊Dic3—54no—
320C4⋊Dic3—58no—
321C4⋊Dic3C22×D514yes—
322Dic3⋊C4—58no—
323Dic3⋊C4—58no—
324Dic3⋊C4—58no—
325Dic3⋊C4—54no—
326Dic3⋊C4—54no—
327Dic3⋊C4C22×D518yes—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C23×C5—31no—
332C23×C5—34no—
333C23×C5—31no—
334C23×C5—62no—
335C23×C5—62no—
336C23×C5C23×D311yescharacteristic
337C2×C4×C5—34no—
338C2×C4×C5—32no—
339C2×C4×C5—38no—
340C2×C4×C5—38no—
341C2×C4×C5—34no—
342C2×C4×C5—42no—
343C2×C4×C5—68no—
344C2×C4×C5—124no—
345C2×C4×C5—122no—
346C2×C4×C5D3×Q814yescomplemented
347C2×C4×C5C23×D314yes—
348C2×C4×C5C23×D312yes—
349C2×Dic5—34no—
350C2×Dic5—34no—
351C2×Dic5—68no—
352C2×Dic5—68no—
353C2×Dic5C23×D314yes—
354C2×Dic5C23×D314yes—
355Dic10—44no—
356Dic10—128no—
357Dic10—124no—
358C22×Q8—154no—
359C23×C4—31no—
360C23×C4—32no—
361C4⋊Q8—54no—
362C4⋊Q8—154no—
363C4⋊Q8—158no—
364C4⋊Q8—154no—
365C4⋊Q8—158no—
366C4⋊Q8—154no—
367#125—54no—
368#125—154no—
369#125—158no—
370#125—158no—
371#125—154no—
372#125—154no—
373C22⋊Q8—54no—
374C22⋊Q8—158no—
375C22⋊Q8—158no—
376C22⋊Q8—154no—
377C22⋊Q8—154no—
378C22⋊Q8—154no—
379#117—52no—
380#117—154no—
381#117—154no—
382#117—152no—
383#117—152no—
384#117—152no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—152no—
390C2×C4⋊C4—152no—
391C2×C4⋊C4—154no—
392C2×C4⋊C4—158no—
393C2×C4⋊C4D3×D511yescharacteristic
394C2×C22⋊C4—154no—
395C2×C42—154no—
396C2×C3×C5—22no—
397C2×C3×C5C23×Q811yescharacteristic
398C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
399C2×C3×C5C2×2−1+411yescharacteristic
400C5×D3—22no—
401C5×D3#54414yescomplemented
402C23×C3C23×D511yescharacteristic
403C22×D3—22no—
404C22×D3—22no—
405C22×D3C2×Dic1014yes—
406C22×D3C23×D511yescharacteristic
407C22×D3C23×D511yescharacteristic
408C3×Q8—204no—
409C2×C3×C4—42no—
410C2×C3×C4—54no—
411C2×C3×C4—54no—
412C2×C3×C4C2×Dic1014yescomplemented
413C2×C3×C4C23×D514yes—
414C2×C3×C4C23×D512yes—
415C2×Dic3—42no—
416C2×Dic3—54no—
417C2×Dic3—54no—
418C2×Dic3C2×Dic1014yescomplemented
419C2×Dic3C23×D514yes—
420C2×Dic3C23×D512yes—
421C4×D3—28no—
422C4×D3—44no—
423C4×D3—108no—
424C4×D3—108no—
425C4×D3C2×Dic1018yes—
426C4×D3C2×Dic1018yescomplemented
427Dic6—208no—
428Dic6—204no—
429C22×C5—21no—
430C22×C5—21no—
431C22×C5—32no—
432C22×C5—32no—
433C22×C5—32no—
434C22×C5—32no—
435C22×C5—68no—
436C22×C5—61no—
437C22×C5—61no—
438C22×C5C2×D3×Q812yes—
439C22×C5C24×D311yescharacteristic
440C4×C5—24no—
441C4×C5—34no—
442C4×C5—64no—
443C4×C5C2×D3×Q814yes—
444Dic5—24no—
445Dic5—24no—
446Dic5—64no—
447Dic5—64no—
448C24—31no—
449C2×Q8—54no—
450C2×Q8—158no—
451C2×Q8—154no—
452C2×Q8—608no—
453C22×C4—31no—
454C22×C4—38no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—34no—
459C22×C4—34no—
460C22×C4—124no—
461C22×C4—154no—
462C22×C4—154no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—34no—
467C4⋊C4—52no—
468C4⋊C4—52no—
469C4⋊C4—54no—
470C4⋊C4—58no—
471C4⋊C4—154no—
472C4⋊C4—154no—
473C4⋊C4—158no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—152no—
477C4⋊C4—152no—
478C4⋊C4—154no—
479C4⋊C4—158no—
480C4⋊C4C2×D3×D514yes—
481C22⋊C4—54no—
482C22⋊C4—154no—
483C22⋊C4—154no—
484C22⋊C4—154no—
485C42—54no—
486C42—154no—
487C42—154no—
488C42—154no—
489C3×C5C2×#54411yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3C22×Dic1012yes—
493C22×C3C24×D511yescharacteristic
494C2×D3—21no—
495C2×D3—21no—
496C2×D3—28no—
497C2×D3C22×Dic1012yes—
498C2×D3C22×Dic1012yes—
499C2×D3#414412yes—
500C2×D3#414712yes—
501C3×C4—24no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4C22×Dic1014yes—
505Dic3—24no—
506Dic3—104no—
507Dic3—104no—
508Dic3C22×Dic1014yes—
509C2×C5—22no—
510C2×C5—34no—
511C2×C5—62no—
512C2×C5C22×D3×Q811yescharacteristic
513C2×C5D3×H(5,𝔽2)11yescharacteristic
514C2×C5D3×2−1+411yescharacteristic
515C23—31no—
516C23—34no—
517C23—31no—
518C23—62no—
519C23—62no—
520C23C22×D3×D511yescharacteristic
521Q8—204no—
522Q8—604no—
523Q8—608no—
524C2×C4—34no—
525C2×C4—32no—
526C2×C4—38no—
527C2×C4—38no—
528C2×C4—34no—
529C2×C4—42no—
530C2×C4—54no—
531C2×C4—54no—
532C2×C4—68no—
533C2×C4—124no—
534C2×C4—122no—
535C2×C4—154no—
536C2×C4—154no—
537C2×C4—308no—
538C2×C4—308no—
539C2×C4D3×Dic1014yescomplemented
540C2×C4C22×D3×D514yes—
541C2×C4C22×D3×D512yes—
542C2×C3—22no—
543C2×C3C23×Dic1011yescharacteristic
544C2×C3C2×#414411yescharacteristic
545C2×C3C2×#414711yescharacteristic
546D3—22no—
547D3#6583414yesdirect product factor
548C5D3×#54411yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—32no—
552C22—32no—
553C22—32no—
554C22—32no—
555C22—68no—
556C22—61no—
557C22—61no—
558C22C2×D3×Dic1012yes—
559C22C23×D3×D511yescharacteristic
560C4—24no—
561C4—34no—
562C4—64no—
563C4—104no—
564C4—104no—
565C4—304no—
566C4—304no—
567C4C2×D3×Dic1014yes—
568C3C2×#6583411yescharacteristic, complemented, Sylow
569C2—22no—
570C2—34no—
571C2—62no—
572C2C22×D3×Dic1011yescharacteristic
573C2D3×#414411yescharacteristic
574C2D3×#414711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×C4⋊C4C22
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#544
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11756259C2semidirect
3. C3×#65834C2semidirect
4. #11754619C2semidirect
7. #11754182C2semidirect
8. D3×#4036C2semidirect
9. D3×#4034C2semidirect
10. #11753370C2semidirect
11. #11753331C2semidirect
19. #91779C22semidirect
20. #91777C22semidirect
27. C3×#4036C22semidirect
28. C3×#4034C22semidirect
32. #91470C22semidirect
33. #91468C22semidirect
39. #91388C22semidirect
40. #91384C22semidirect
45. #91346C22semidirect
46. #91343C22semidirect
49. #91328C22semidirect
50. #91327C22semidirect
60. #65834D3direct (N × H)
70. C2×C4×C5×D3Q8semidirect
146. #4036C2×D3semidirect
152. #4034C2×D3semidirect
161. C2×C3×C4×C5C2×Q8semidirect
168. C2×C5×Dic3C2×Q8semidirect
174. C4×C5×D3C2×Q8semidirect
300. C2×C4×D3Dic10semidirect
346. C2×C4×C5D3×Q8semidirect
401. C5×D3#544semidirect
412. C2×C3×C4C2×Dic10semidirect
418. C2×Dic3C2×Dic10semidirect
426. C4×D3C2×Dic10semidirect
489. C3×C5C2×#544semidirect
539. C2×C4D3×Dic10semidirect
547. D3#65834direct (N × H)
548. C5D3×#544semidirect
568. C3C2×#65834semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117562592
C2×C5×D3×C4⋊C42
C3×#658342
#117546192
D3×#40722
D3×#40702
#117541822
D3×#40362
D3×#40342
#117533702
#117533312
C2×#658343
D3×#5445